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Question

Three waves of amplitude 10μ m,4μ m and 7μ m arrive at a point with successive phase difference of π/2. The amplitude of the resultant wave is

A
2μm
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B
7μm
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C
5μm
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D
1
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Solution

The correct option is D 5μmGiven,Amplitude of the waves are,a1=10μm,a2=4μm,a3=7μmand the phase difference between 1st and 2nd wave is π2 and that between 2nd and 3rd wave is π2. Therefore, phase difference between 1st and 3rd is π. Combining 1st with 3rd, their resultant amplitude will beA21=a21+a23+2a1a3cosϕorA1=√102+72+2×10×7cosπ=√100+49−140=√9=3μm in the direction of first.Now combining this with 2nd wave we get the resultant wave,A2=A21+a22+2A1a2cosπ2orA=√32+42+2×3×4cos902=√9+16=5μm

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